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(1579393975)_{1386}1 is PrP

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  • d.broadhurst@open.ac.uk
    As Phil indicated, it doesn t take much time or brain merely to *find* a PrP of the type that I guess Harvey has in mind to prove. It was as simple as ABC to
    Message 1 of 4 , Sep 24, 2001
      As Phil indicated, it doesn't take much time or brain merely
      to *find* a PrP of the type that I guess Harvey has in mind
      to prove. It was as simple as ABC to find

      (1579393975)_{1386}1

      which is a 13861-digit palindromic PrP,
      all of whose digits are odd,
      with no neighbouring digits equal
      (contrast with top-20 palindromes)

      PFGW Version 20010818.Win_Dev
      (Beta software, 'caveat utilitor')
      Primality testing 15793939750*R(13860)/R(10)+1
      [N-1, Brillhart-Lehmer-Selfridge]
      Reading factors from helper file HD13860.fac
      Running N-1 test using base 3
      Running N-1 test using base 7
      Running N-1 test using base 11
      Calling Brillhart-Lehmer-Selfridge with factored part 29.59%
      15793939750*R(13860)/R(10)+1 is PRP!
      (2206.190000 [Rosinante] seconds)

      It may be proven prime with 4 more things:
      another prime factor of 10^13860-1;
      and another (if first less than p57);
      a rerun of Pfgw with these factors;
      a Konyagin-Pomerance cubic test.

      David
    • d.broadhurst@open.ac.uk
      I got trusty old Rosinante to redo all the Pari/Pfgw/Tx tests for the 13861-digit all-odd-digit palindrome (1579393975)_{1386}1 =
      Message 2 of 4 , Oct 2, 2001
        I got trusty old Rosinante to redo all the Pari/Pfgw/Tx
        tests for the 13861-digit all-odd-digit palindrome

        (1579393975)_{1386}1 = 15793939750*(10^13860-1)/(10^10-1)+1

        and then I packed them in

        http://groups.yahoo.com/group/primenumbers/files/Factors/djb13860.zip

        together with a demo that my Pari KP code replicates
        Andy Steward's largest-ever KP test (at 10619 digits).

        The KP cubic for the palindrome disagrees with Satoshi's.
        But maybe he did not use all the factors?

        Satoshi: please check that you ran with
        F1=log(F)/log(N)=0.3012668 where F contains
        all known prime divisors of N-1.

        Did you include repeats,
        and also factors of 15793939750?
        I did.

        David
      • Satoshi TOMABECHI
        David, be glad! I tested using file hd13860p.fac including factors of 15793939750. The result by my program conincides with PARI s output at any point. One of
        Message 3 of 4 , Oct 2, 2001
          David, be glad!

          I tested using file hd13860p.fac including factors of 15793939750.
          The result by my program conincides with PARI's output at any point.

          One of the roots is 3.309279218*10^(-1421).

          > Did you include repeats,
          > and also factors of 15793939750?
          > I did

          Yes, previous test didn't use factors of 15793939750.
          But it was a 30.05% proof.

          Satoshi Tomabechi
        • d.broadhurst@open.ac.uk
          ... I obey:-)
          Message 4 of 4 , Oct 2, 2001
            Satoshi TOMABECHI commanded:
            > David, be glad!
            I obey:-)
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